Reliable communication over highly connected noisy networks

Noga Alon, Mark Braverman, Klim Efremenko, Ran Gelles, Bernhard Haeupler

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We consider the task of multiparty computation performed over networks in the presence of random noise. Given an n-party protocol that takes R rounds assuming noiseless communication, the goal is to find a coding scheme that takes R rounds and computes the same function with high probability even when the communication is noisy, while maintaining a constant asymptotic rate, i.e., while keeping lim inf n , R R/ R positive. Rajagopalan and Schulman (STOC ’94) were the first to consider this question, and provided a coding scheme with rate O(1 / log (d+ 1)) , where d is the maximal degree in the network. While that scheme provides a constant rate coding for many practical situations, in the worst case, e.g., when the network is a complete graph, the rate is O(1 / log n) , which tends to 0 as n tends to infinity. We revisit this question and provide an efficient coding scheme with a constant rate for the interesting case of fully connected networks. We furthermore extend the result and show that if a (d-regular) network has mixing time m, then there exists an efficient coding scheme with rate O(1 / m3log m). This implies a constant rate coding scheme for any n-party protocol over a d-regular network with a constant mixing time, and in particular for random graphs with n vertices and degrees nΩ ( 1 ).

Original languageEnglish (US)
Pages (from-to)505-515
Number of pages11
JournalDistributed Computing
Volume32
Issue number6
DOIs
StatePublished - Dec 1 2019

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Hardware and Architecture
  • Computer Networks and Communications
  • Computational Theory and Mathematics

Keywords

  • Coding theory
  • Computation with noise
  • Interactive coding
  • Random noise

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